You could build it with any power supply from 6 to 12 volts if you do not have a broken drill laying around.
This is a total hardware hack. I know it looks like crap. We were having a party and I wanted a prop that would scare people. I threw it together in about 2 hours. I've spent three times longer documenting the build than I did actually building it.
I have a really well stocked junk collection, so everything that I used to build this was actually laying around the shop before I started building it. The design is very flexible and will work with whatever junk you have.
Step 1: The power source
I relocated the PWM power transistor to the side of the drill handle, because there was no room for it inside after the top of the handle broke off.
I attached two heavy (16 GA) wires to the power output of the drill speed control.
Step 2: The Filter
Step 3: The oscillating relay
The curly bits of wire serve as RF chokes and reduce radio frequency interference.
I put hot glue over the pins to insulate and protect them.
Step 4: The Coil
Step 5: The probe
I took a section of a spring and bent up the end of it until it was kinked and twisted. Then I forced this into the end of the coil with a twisting motion. This made a spring friction mount for the rod. The rod stays inside the spring really well.
Step 6: The Ground wires
The whole thing is pretty much held together with hot glue.
Step 7: Using it
When the power is at a low setting, the relay points just chatter a little, but there is still several hundred volts at the probe. The power control has a low range, where the relay is chattering, and a high range, where the relay is getting a full stroke and the IGN coil is getting saturated.
There is an optimal setting of the "throttle". When you change the power level you are changing the "dwell" time of the relay points. The dwell is the time that the energy charges up in the winding before the points open and collapse the field. It is the abrupt collapse of the field that creates the high voltage flyback effect. The size of the spark gap also matters. If the gap is larger the voltage can ring up to a higher peak before it discharges. If the gap is too big, the air will never breakdown and there will be no arc. Remember that an arc in air is about 10,000 volts per centimeter, so I have seen as much as 45,000 volts from this coil.
THIS CAN REALLY HURT YOU!